ABSTRACT
This chapter analyses the problem of the asymptotic convergence of scattering states for a collision of two structureless particles. For scattering theory, convergence of state vectors and operators is required to be strong, as a more stringent condition than weak convergence. In non-relativistic collisions, the velocity of the scattering particles is negligible with respect to the speed of light c. The accomplished analysis is of direct use for studying the asymptotic convergence of scattering states. An adequate physical interpretation of the obtained results is in order. The asymptotically free scattering states, which are introduced in an unambiguous manner, will become of decisive importance for a proper physical interpretation of the obtained results. The obtained strong limit of the quantum-mechanical free wave packet U0(t)χ represents a physically intuitive criterion for the asymptotic freedom, which encompasses the essential requirements imposed on the outgoing and incoming wave packets.
